Presidential aides, exuding increased confidence that Bert Lance can be saved, are looking to Senate Majority Leader Robert C. Byrd (D-W.Va.) as a key barometer of whether Lance has defended himself well enough to remain director of the Office of Management and Budget.

Lance's future with the government, according to a senior White House official who has been delighted with the budget director's performance through two days of hearings, now rests with the sentiment of the Senate, not public opinion polls or media demands for his resignation.

In view of White House officials, that sentiment has shifted dramatically in Lance's favor as he has defended himself before the Senate Governmental Affairs Committee. Whether it has shifted enough for Lance to survive as OMB director is still not clear and may hinge on Byrd's reading of his colleague's attitudes.

One week ago, Byrd said Lance should resign, that his "effectiveness has been destroyed," a statement the White House officials believe Byrd may not be prepared to repeat now.

"If the sentiment of the Senate shifts, there is a possibility that Sen. Byrd would take a different view," one official said.

The Majority Leader was not talking yesterday, saying he would withhold comment until after the Lance hearings are completed. But that silence, contrasted with his statement of a week ago, seemed to confirm the White House view that Byrd has stepped back into a "wait-and-see" attitude on the matter.

President Carter left late yesterday afternoon to spend the weekend at Camp David, Md. If the Lance hearings wind up today, the decision Carter has promised on Lance's future could be made there in the solitude of the Catoctin Mountains.

A senior presidential aide said yesterday that Carter's decision will rest on two major factors.

The first is a moral or ethical judgement - Has Lance done anything wrong?

Although less effusive than he has been in the past, the President said Thursday he had no reason to believe that Lance "is dishonest, incompetent or acted unethically." That amounted to a moral endorsement even as Lance began his spirited defense.

"I don't think that's going to change," the presidential aide said, confirming the widespread view that all the allegations against Lance have not touched the President's deep faith in his close friend and confident.

If that continues to be Carter's moral judgment, then Lance's fate will rest on the second factor - a political judgment of his continuing effectiveness as OMB director.

"Politically, it's much more difficult judgment - whether the weight of these allegations makes it difficult for him to be an effective OMB director," the official said. "Congressional sentiment has a lot to do with it."

"And," he continued, "we've got a practical problem - Robert C. Byrd. His judgment [last week] was based on the sentiment of the Senate. Maybe the sentiment of the Senate has changed. But looking down the road, we've got to have a good relationship with thos people, with Byrd, with that committee, with the whole Senate . . . If 75 people in the Senate say Bert can't be an effective OMB director, then he's in trouble.We're not blind to that."

But White House aides do not believe anything near 75 senators are against Lance. One said the Senate now seems "polarized" over the issue and that Lance, always personally popular, "has whole cheering sections up there."

"Of course, a lot of people don't like Percy anyway," the official said, a reference to one of Lance's harshest critics, Sen. Charles H. Percy (R-Ill.).

The upbeat mood of White House aides reflected a belief among many of them that the President has already won an important victory by sticking with Lance through a torrent of unfavorable news stories and demands for his resignation.

"Personally, it was important, that we show strength through this," one of them said. "It was important that we show that other people, including the media and the Congress, don't make decisions for us. We make our own decisions.

"It is important for a guy to withstand allegations and survive," the aide continued. "Symbolically, that's what's been important about Bert to us."

Another factor in the White House defense of Lance, he said, has been the feeling that the portrayal of Lance in the news as a "shady, bumbling country banker" has reflected badly on the President's choice of him as budget director.

But the public perception of Lance as reflected in the polls will not be the deciding factor, the aide said.

"You can show that two of every three people are against Lance, but that's the poorest argument you can made, to us or to Carter," he said. "That just makes us dig our heels in deeper."

According to White House press secretary Jody Powell, public opinion, at least as measured by calls to the White House, has shifted in Lance's favor. Powell said the calls have shifted from 64 per cent against Lance remaining as OMB director one day earlier this week to 84 per cent who support him as measured by calls yesterday.